WASHINGTON — Hillary Rodham Clinton insists she hasn't decided whether she'll run again for president, but she's laying out more reasons to run than not during her coast-to-coast book tour.

The Republicans' inquiry into the deadly raid in Benghazi emboldens her, she says. She knows how not to run a campaign after losing the 2008 Democratic nomination to Barack Obama. And she'd be doing something for the women and girls she felt she let down that year, and perhaps, she suggests, be more effective in the struggle by both parties to get gender politics right.

"We live with a double standard," Clinton told ABC News as she kicked off a tour for "Hard Choices," her memoir. "People ought to think about their own daughters, their own sisters, their own mothers, when they make comments about women in public life."

Her main reason to sit 2016 out?

"I really like my life," Clinton said. "I like what I'm doing. I'm thrilled about becoming a grandmother in the fall. I have lots of hopes for what that means to me and my family."

However, in the next breath, she notes that having a grandchild — daughter Chelsea is expecting — does not put the White House off-limits.

In highly choreographed appearances and interviews, Clinton is making quite clear that she already has given serious consideration to running for president, again. She has a ready-made network of supporters and fundraisers and, unlike in 2008, no real competition for the Democratic nomination.

The temptation to run is clear. Asked by ABC News about the Republican probes into her knowledge and role in the response to the deadly raid on the U.S. compound in Benghazi, Libya, Clinton leaned forward and said they provided an incentive.

"It's more of a reason to run, because I do not believe our great country should be playing minor league ball," she said emphatically. "We ought to be in the majors."

She says she now knows how not to run a campaign after the bitter experience of having watched Obama beat her in Iowa and arriving in New Hampshire dumbfounded.

"I don't think I ever said, yes, you may have known me for eight years, but I don't take anything for granted," Clinton told ABC. "I have to earn your support."

View full sizeHillary Clinton signs a copy of her memoir at the Central Branch of the Free Library of Philadelphia Free on June 13, 2014. Associated Press

And in her memoir, Clinton suggests that some in her own party got gender politics wrong. After Republican presidential nominee John McCain picked Sarah Palin to be his running mate, aides to Obama asked Clinton to attack Palin, Clinton wrote.

"I said, 'Attack her for what? For being a woman?'" Clinton said. She said she told the Obama campaign, "There'll be plenty of time to do what I think you should do in politics, which is draw distinctions."

And as she tours the country and appears before audiences of autograph-seekers and admirers, Clinton and the public are becoming reacquainted, for better or worse.

Polls taken as she launched her publicity tour show a slight slide in Clinton's favorability rating, though most Americans continue to view her in a positive light. A Gallup Poll on the eve of her memoir's release found 54 percent of Americans viewed her favorably, down from 59 percent in February. As secretary of state, Clinton's favorability consistently topped 60 percent, according to Gallup.

Clinton says she finds the prospect of running compelling for the mere chance it offers to help Americans find economic opportunities that elude them. There are political opportunities, too.

In interviews during the first week of her book tour, the former first lady confronted a pair of potential political weaknesses in an effort, perhaps, to put them behind her.

Asked in the ABC interview about Monica Lewinsky, the former White House intern whose affair with Clinton's husband bill led to his impeachment and Senate acquittal, Clinton answered that she doesn't give her much thought, wished Lewinsky well and acknowledged that interviewer Diane Sawyer had a right to ask the question.

"I have moved on," Clinton said, with none of the clipped, not-your-business tone she's used in the past.

However, on National Public Radio on Thursday, Clinton scrapped with "Fresh Air" host Terry Gross for questioning her motivation behind shifting last year from opposing to supporting gay marriage.

"No, I don't think you are trying to clarify," Clinton scolded Gross. "I think you are trying to say that I used to be opposed and now I am in favor and I did it for political reasons. And that's just flat wrong."